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3 years ago

13

Write the quadratic equation whose roots are -2 and 1, and whose leading coefficient is 4 .

1 answer:

Kaylis [27]3 years ago

7 0

Answer: the equation is

4x^2 + 4x - 12

Step-by-step explanation:

A quadratic equation is an equation in which the highest power of the unknown is 2.

The general form of a quadratic equation is expressed as

ax^2 + bx + c

Where

a is the leading coefficient

c is a constant

Assuming we want to write the quadratic equation in x, from the information given, the roots which are given are -2 and 1 and the leading coefficient is 4.

Therefore, the linear factors of the quadratic equation will be (x+2) and (x-1)

the equation becomes

(x+2)(x-1)

= x^2 - x +2x - 3

= x^2 + x - 3

Given a leading coefficient of 4, we will multiply the quadratic expression by 4. It becomes

4(x^2 + x - 3)

= 4x^2 + 4x - 12

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5 0

3 years ago

5.Find the roots of the parabola given by the following equation.

snow_tiger [21]

Answer:

Part 5) The roots are x=-3 and x=1.5

Part 6) The solution on a number line is the shading area below of the line y=-1/3 (close circle)

Step-by-step explanation:

Part 5) Find the roots of the parabola given by the following equation

$2x^{2} +5x-9=2x$

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$2x^{2}+5x-2x-9=0$

$2x^{2}+3x-9=0$

so

$a=2\\b=3\\c=-9$

substitute in the formula

$x=\frac{-3(+/-)\sqrt{3^{2}-4(2)(-9)}} {2(2)}$

$x=\frac{-3(+/-)\sqrt{81}} {4}$

$x=\frac{-3(+/-)9} {4}$

$x=\frac{-3(+)9} {4}=1.5$

$x=\frac{-3(-)9} {4}=-3$

therefore

The roots are x=-3 and x=1.5

Part 6) Solve the inequality and graph the solution on a number line.

$-3(5y-4)\geq 17$

Solve for y

$-15y+12\geq 17$

Subtract 12 both sides

$-15y\geq 17-12$

$-15y\geq 5$

Multiply by -1 both sides

$15y\leq -5$

Divide by 15 both sides

$y\leq -1/3$

The solution is the interval -----> (-∞, -1/3]

All real numbers less than or equal to negative one third

The solution on a number line is the shading area below of the line y=-1/3 (close circle)

The graph in the attached figure

7 0

3 years ago

otez555 [7]

use a calculator it's way easier but here is the answer

7 0

2 years ago

I want to put $580 until I saving account for one year. The rate of interest On the account was 6 1/2%. How much was the interes

Vanyuwa [196]

Answer:

The amount of interest earned for the year is $37.7

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents principal or amount invested.

T represents the time

R represents the interest rate

I represents the interest

From the information given,

You want to put $580 into a saving account for 1 year. This means that

P = $580 and

T = 1 year

R = 6 1/2 = 6.5%

I = (580× 6.5×1)/100 = $37.7

5 0

4 years ago

Which property is used in the following equation?<br> 3(7+4)=21+12

lakkis [162]

I hope this helps you

8 0

4 years ago

Read 2 more answers